The Hilton is an incongruously modern building on Castle Hill in Buda (or is it Pest?), but close to the historical museum, St. Stephen Church, and traditional restaurants. The public baths may be worth a visit for the mineral waters or massage, and aren't far away. If you want to see Soviet-era statuary, it has all been moved to a "graveyard" at the edge of town; though I haven't been there myself, it is said to be an interesting place to visit. I did take the suburban train to Szentendre (St. Andrew), a well preserved village with pastel painted houses (and inflated prices for linens and glassware). I had very little trouble getting around with just a Hungarian phrase book. Have fun!